Ratios
Understanding Equivalent Ratios
Multiple Ratio Relationships
Multiplication Patterns in Ratio Relationships
Rates
Solving Rate Problems
The Value of A Ratio
Percent and Finding The Percents
Solving Multi Step Rates
Speed
Units of Measurements
100
A classroom has 12 girls and 8 boys. What is the ratio of girls to boys?
A. 8:12
B. 12:8
C. 12:20
D. 8:20
B: 12:20
100
A fruit punch recipe uses 2 cups of orange juice for every 3 cups of pineapple juice. Which ratio is equivalent to 2:3?
A. 4:5
B. 4:6
C. 5:6
D. 6:8
B: 4:6
100
A snack mix uses 3 cups of pretzels for every 2 cups of crackers. It also uses 4 cups of crackers for every 1 cup of popcorn.
If the mix contains 12 cups of pretzels, how many cups of popcorn are needed?
A. 2 cups
B. 4 cups
C. 6 cups
D. 8 cups
A: 2 cups
100
Tyler says the ratios 5:8 and 15:16 are equivalent because he multiplied 5 by 3 and 8 by 2.
What mistake did Tyler make?
A. He should have added instead of multiplied.
B. He needed to multiply both quantities by the same factor.
C. Ratios cannot be multiplied.
D. He should have divided 5 by 8.
B. He needed to multiply both quantities by the same factor.
100
A car travels 180 miles in 3 hours. What is the car's unit rate?
A. 45 miles per hour
B. 60 miles per hour
C. 90 miles per hour
D. 540 miles per hour
B: 60 MILES PER HOURS
100
Jordan types 240 words in 6 minutes. At this rate, how many words does Jordan type per minute?
A. 30 words
B. 40 words
C. 46 words
D. 60 words
B: 40 words
100
A fruit punch recipe uses 8 cups of orange juice for every 5 cups of pineapple juice. What does the ratio (8:5) mean?
A. There are 8 total cups of juice.
B. For every 8 cups of orange juice, there are 5 cups of pineapple juice.
C. There are 5 more cups of orange juice than pineapple juice.
D. The recipe always contains 13 cups.
B. For every 8 cups of orange juice, there are 5 cups of pineapple juice
100
A school has 200 sixth-grade students. 35% of the students participate in a school club. How many sixth graders participate in a club?
A. 35
B. 65
C. 70
D. 165
C: 70
100
A grocery store sells 4 pounds of apples for $7.20. Marcus buys 7 pounds at the same rate. How much will he pay?
A. $10.80
B. $12.60
C. $14.40
D. $15.20
B: $12.60
100
Jayden rides his bicycle 36 miles in 3 hours. If he continues at the same speed, how far will he travel in 5 hours?
A. 48 miles
B. 50 miles
C. 60 miles
D. 72 miles
C- 60 miles
100
A rope is 6 yards long. Since 1 yard = 3 feet, how many feet long is the rope?
A. 2 feet
B. 9 feet
C. 18 feet
D. 24 feet
C: 18 feet
200
At a school dance, there are 15 sixth graders and 10 seventh graders. What is the ratio of sixth graders to all students?
A. 15:10
B. 10:15
C. 15:25
D. 25:15
C: 15:25
200
Which pair of ratios is equivalent?
A. 3:5 and 6:8
B. 4:7 and 8:14
C. 2:9 and 6:18
D. 5:6 and 15:20
B. 4:7 and 8:14
200
At a school dance, the ratio of boys to girls is 3:4. The ratio of girls to teachers is 8:1.
If there are 24 boys, how many teachers are at the dance?
A. 2
B. 4
C. 6
D. 8
B: 4
200
The ratio of red balloons to blue balloons is 4:7. If both quantities are multiplied by 3, what is the new ratio?
A. 7:10
B. 8:14
C. 12:21
D. 16:28
C. 12:21
200
A 6-pack of sports drinks costs $9.00. What is the cost per sports drink?
A. $1.25
B. $1.50
C. $2.00
D. $3.00
B: $1.50
200
A grocery store sells 5 pounds of apples for $8.75. What is the cost per pound?
A. $1.25
B. $1.50
C. $1.75
D. $2.25
C: $1.75
200
Two students are comparing their reading rates.
- Maria: 48 pages in 4 hours
- Jordan: 65 pages in 5 hours
Who reads at the greater rate?
A. Maria, because (48>65)
B. Maria, because she reads 12 pages per hour
C. Jordan, because he reads 13 pages per hour
D. They read at the same rate.
C. Jordan, because he reads 13 pages per hour
200
A store has 80 backpacks. 25% of the backpacks are blue. How many backpacks are blue?
A. 20
B. 25
C. 32
D. 55
A: 20
200
Store A sells 6 notebooks for $10.50. Store B sells 8 notebooks for $13.20. Jayden needs 24 notebooks. Which store will cost less, and by how much?
A. Store A by $2.40
B. Store B by $2.40
C. Store A by $4.80
D. Store B by $4.80
Answer: B
Store A: $1.75 each × 24 = $42.00
Store B: $1.65 each × 24 = $39.60
Difference = $2.40
200
Car A travels 180 miles in 3 hours. Car B travels 260 miles in 5 hours. Which statement is correct?
A. Car A is faster by 8 mph.
B. Car B is faster by 8 mph.
C. Car A is faster by 52 mph.
D. Both cars travel at the same speed.
A. Car A is faster by 8 mph
200
A recipe requires 6 cups of milk. If 1 cup = 8 fluid ounces, how many fluid ounces of milk are needed?
A. 14 fl oz
B. 24 fl oz
C. 48 fl oz
D. 64 fl oz
C: 48 fl oz
300
Mr. Justice has 6 blue pens and 10 black pens. What is the ratio of black pens to blue pens?
A. 6:10
B. 10:6
C. 6:16
D. 10:16
B: 10:6
300
Complete The Ratio Table:
Apples: 3 , 6, 9, ?
Oranges: 5, 10, 15, 20
A. 10
B. 12
C. 15
D. 18
B: 12
300
A school club has a ratio of boys to girls of 2:3. The ratio of girls to adults is 6:1.
There are 36 girls at an event. Which statement is correct?
A. There are 18 boys and 6 adults.
B. There are 24 boys and 6 adults.
C. There are 24 boys and 12 adults.
D. There are 54 boys and 6 adults.
B. There are 24 boys and 6 adults
300
A bakery uses 5 cups of flour for every 2 batches of muffins. Which multiplication pattern could be used to find the amount of flour needed for 8 batches?
A. Multiply both quantities by 2
B. Multiply both quantities by 3
C. Multiply both quantities by 4
D. Multiply only the number of batches by 4
C. Multiply both quantities by 4
300
How far will the cyclist travel in 5 hours?
A. 48 miles
B. 50 miles
C. 60 miles
D. 72 miles
C: 60 miles
300
Store A sells 8 sports drinks for $12.00. Store B sells 6 sports drinks for $8.40. Which store has the better price per drink, and how much less is each drink?
A. Store A by $0.10
B. Store B by $0.10
C. Store A by $0.20
D. Store B by $0.20
B. Store B by $0.10
300
Movie Theater A sells 3 tickets for $27. Movie Theater B sells 5 tickets for $40.
Which statement is correct?
A. Theater A is cheaper because 3 is less than 5.
B. Theater A is cheaper because tickets cost $9 each.
C. Theater B is cheaper because tickets cost $8 each.
D. Both theaters charge the same price per ticket.
C. Theater B is cheaper because tickets cost $8 each.
300
A store sells a pair of shoes for $80. The shoes are discounted by 25%. What is the sale price?
A. $20
B. $55
C. $60
D. $75
C: $60
Reasoning: 25% of $80 = $20. Then $80 − $20 = $60.
300
A runner completes 6 miles in 48 minutes. She continues at the same rate until she has run 10 miles total. How many additional minutes will she need?
A. 24 minutes
B. 30 minutes
C. 32 minutes
D. 40 minutes
Answer: C
48 ÷ 6 = 8 minutes per mile; 4 additional miles × 8 = 32 minutes
300
Correct Answer: A
300
Imogene needs to ship 5 identical books that have a total weight of 7.5 pounds. What is the weight, in ounces, of each book?
A: 12 ounces
B: 32 ounces
C: 24 ounces
D: 48 ounces
Hint: 1 pound = 16 ounces
C: 24 ounces
400
A fruit basket contains 8 apples and 3 oranges. Complete the sentence:
For every _____ apples, there are _____ oranges.
8 Apples, 3 Oranges
400
Jamal says that 6:10 and 9:15 are equivalent ratios. Which explanation best supports Jamal's claim?
A. Both ratios have a difference of 4.
B. Both ratios can be simplified to 3:5.
C. Both ratios contain even numbers.
D. 6 + 10 = 9 + 15.
B. Both ratios can be simplified to 3:5
400
A fruit basket contains apples, oranges, and bananas. The ratio of apples to oranges is 4:3, and the ratio of oranges to bananas is 3:2.
If there are 16 apples, how many bananas are there?
A. 6
B. 8
C. 12
D. 24
B: 8
400
Which ratio is NOT equivalent to 6:9?
A. 12:18
B. 18:27
C. 24:36
D. 30:40
D: 30:40
400
Store A sells 8 notebooks for $12.00. Store B sells 6 notebooks for $8.40. Which store has the better price per notebook?
A. Store A because each notebook costs $1.50
B. Store B because each notebook costs $1.40
C. Store A because 8 notebooks is more than 6 notebooks
D. Both stores have the same unit price
B. Store B because each notebook costs $1.40
400
A school cafeteria uses 18 cartons of milk for every 24 students. There are 72 students eating lunch. How many cartons of milk are needed if the rate remains the same?
A. 36
B. 48
C. 54
D. 60
C: 54
400
Store A sells 6 sports drinks for $9. Store B sells 10 sports drinks for $14.
Which store has the better price per drink, and why?
A. Store A because each drink costs $1.50.
B. Store B because each drink costs $1.40.
C. Store A because 6 is less than 10.
D. Store B because $14 is greater than $9.
B. Store B because each drink costs $1.40.
400
At a school, 45% of 240 students ride the bus. The remaining students arrive another way. How many students do notride the bus?
A. 108
B. 120
C. 132
D. 195
C: 132
400
Two water pumps are being compared.
- Pump A fills 120 gallons in 8 minutes.
- Pump B fills 168 gallons in 12 minutes.
If each pump runs for 24 minutes, how many more gallons will the faster pump fill?
A. 12 gallons
B. 24 gallons
C. 36 gallons
D. 48 gallons
Answer: B
Pump A = 15 gal/min → 360 gallons
Pump B = 14 gal/min → 336 gallons
Difference = 24 gallons
400
What value belongs in the table, and why?
A. 275 miles because the car travels 55 mph.
B. 330 miles because the car travels 55 mph.
C. 440 miles because the distance doubles every 2 hours.
D. 660 miles because (110×6=660)
B: 330 Miles because the car travels 55 mph
400
A package weighs 80 ounces. If 16 ounces = 1 pound, how many pounds does the package weigh?
A. 4 lb
B. 5 lb
C. 6 lb
D. 8 lb
B: 5 Ib
500
The ratio of chocolate cupcakes to vanilla cupcakes is 4:7. Which statement is correct?
A. For every 4 chocolate cupcakes, there are 7 vanilla cupcakes.
B. For every 7 chocolate cupcakes, there are 4 vanilla cupcakes.
C. There are exactly 11 cupcakes.
D. There are 4 more vanilla cupcakes.
A. For every 4 chocolate cupcakes, there are 7 vanilla cupcakes
500
A sports drink is made using 2 scoops of powder for every 5 cups of water. If a coach uses 8 scoops of powder, how many cups of water should be used to keep the ratio equivalent?
A. 10 cups
B. 15 cups
C. 20 cups
D. 25 cups
C: 20 cups
500
Two students are solving this problem:
The ratio of chocolate cupcakes to vanilla cupcakes is 2:5. The ratio of vanilla cupcakes to strawberry cupcakes is 10:3.
Jasmine says: The combined ratio is 2:5:3.
Marcus says: The combined ratio is 4:10:3.
Who is correct, and why?
A. Jasmine, because you can combine the two ratios without changing them.
B. Marcus, because the number representing vanilla must be equal in both ratios.
C. Jasmine, because 2 + 5 = 7.
D. Marcus, because every ratio must begin with an even number.
B. Marcus, because the number representing vanilla must be equal in both ratios.
500
A recipe uses 2 cups of rice for every 5 people. A chef needs to serve 20 people. Which strategy correctly determines the amount of rice needed?
A. Multiply 2 and 5 by 4, giving 8 cups for 20 people.
B. Multiply only 5 by 4, giving 2 cups for 20 people.
C. Add 4 to both quantities, giving 6 cups for 9 people.
D. Multiply 2 by 20, giving 40 cups.
A. Multiply 2 and 5 by 4, giving 8 cups for 20 people
500
Bus A travels 150 miles in 3 hours. Bus B travels 220 miles in 4 hours. Which statement is correct?
A. Bus A is faster by 5 mph.
B. Bus B is faster by 5 mph.
C. Bus A is faster by 10 mph.
D. Both buses travel at the same speed.
B: Bus B is faster by 5 mph.
500
Tyler claims that a car traveling 210 miles in 3.5 hours is moving faster than a car traveling 260 miles in 4 hours.
Which statement best evaluates Tyler's claim?
A. Tyler is correct because 210 ÷ 3.5 = 70 mph.
B. Tyler is correct because 210 miles is farther.
C. Tyler is incorrect because the first car travels 60 mph and the second travels 65 mph.
D. Tyler is incorrect because both cars travel 60 mph.
C. Tyler is incorrect because the first car travels 60 mph and the second travels 65 mph.
500
Two machines fill bottles.
- Machine A fills 24 bottles in 3 minutes.
- Machine B fills 35 bottles in 5 minutes.
Which machine works faster?
A. Machine A because it fills 8 bottles per minute.
B. Machine B because it fills 7 bottles per minute.
C. Machine B because 35 is greater than 24.
D. They work at the same rate.
A. Machine A because it fills 8 bottles per minute
500
A store advertises:
SALE: 35% OFF!
A bicycle originally costs $240. Carlos says the sale price will be $156. Is Carlos correct?
A. Yes, because the discount is $84 and (240-84=156).
B. Yes, because 35% of 240 is $156.
C. No, because the sale price is $84.
D. No, because the sale price is $205.
A. Yes, because the discount is $84 and (240-84=156)
500
A family drives 210 miles in 3.5 hours. They have 150 miles remaining and continue at the same rate. Including a 30-minute rest stop, how much time will the entire trip take?
A. 5.5 hours
B. 6 hours
C. 6.5 hours
D. 7 hours
Answer: C
210 ÷ 3.5 = 60 mph; 150 ÷ 60 = 2.5 hours; 3.5 + 2.5 + 0.5 = 6.5 hours
500
Vehicle A travels 300 miles in 5 hours. Vehicle B travels 280 miles in 4 hours. Both vehicles continue at their constant speeds for 2 more hours. How much farther will Vehicle B travel than Vehicle A during those 2 hours?
A. 10 miles
B. 20 miles
C. 40 miles
D. 60 miles
B: 20 miles
500
A bag of rice weighs 4 kilograms. How many grams does the bag weigh?
A. 40 g
B. 400 g
C. 4,000 g
D. 40,000 g
C: 4,000 g